Problem: Solve for $x$ : $x^2 - x - 12 = 0$
Answer: The coefficient on the $x$ term is $-1$ and the constant term is $-12$ , so we need to find two numbers that add up to $-1$ and multiply to $-12$ The two numbers $-4$ and $3$ satisfy both conditions: $ {-4} + {3} = {-1} $ $ {-4} \times {3} = {-12} $ $(x {-4}) (x + {3}) = 0$ Since the following equation is true we know that one or both quantities must equal zero. $(x -4) (x + 3) = 0$ $x - 4 = 0$ or $x + 3 = 0$ Thus, $x = 4$ and $x = -3$ are the solutions.